Precise timekeeping is important in communications and navigation satellite systems. The long-term frequency stability of the atomic standards deployed in those systems can have a significant impact on overall system performance. For example, timekeeping errors that arise in the Milstar system, where atomic clocks are deployed on the satellites and at the ground control stations, will influence system performance during autonomy and endurance periods. Similarly, timekeeping is critical for the Global Positioning System (GPS), where atomic clocks are also deployed on the satellites, because a one microsecond time error can lead to a thousand foot positioning error. Though present atomic clock technology allows these systems to meet their specifications, future systems and system-upgrades will undoubtedly require improvements. Increasing timekeeping precision for small, lightweight satellite clocks would lengthen the autonomy period for Milstar satellites, and would reduce the workload at ground stations conducting satellite time maintenance. Also, the GPS would benefit from improved miniature atomic clocks, because these devices could be incorporated into hand held GPS receivers, thereby increasing the acquisition rate of GPS navigational data. Commercial applications of precise time and frequency are increasing as commercial communications systems seek to more finely divide the radio frequency spectrum for increased traffic.
Rubidium (Rb) atomic clocks are flown on the GPS and Milstar satellites, and are the smallest and lightest atomic clocks presently available. The long term timekeeping behavior of these standards may be limited by variations of microwave power used to excite the Rb atoms of the atomic clock. In a Rb atomic clock, microwave power fluctuations are coupled to the atomic clock output frequency consequently causing a phenomenon known as the position shift effect. In an atomic clock, the output frequency provides a tick rate of the clock. Any changes in the output frequency causes the atomic clock to either run too slow or too fast. For Rb atomic clocks, a single dB change of microwave power can cause the clock to lose or gain a little over two microseconds every day. Navigational missions require timekeeping stability at the nanosecond level and future needs will seek time accuracy at the microsecond level for periods of many weeks.
The signal in a Rb atomic clock is derived from a vapor of atoms contained within a glass resonance cell, and in a process called optical pumping, lamp light or laser light creates an atomic population imbalance among the atomic ground state sublevels amenable to atomic clock signal generation. Examples of atomic systems include those disclosed in U.S. Pat. No. 4,425,653 entitled Atomic Beam Device using Optical Pumping, and U.S. Pat. No. 5,146,184 entitled Atomic Clock System with Improved Servo Systems. U.S. Pat. No. 5,657,340 entitled Rubidium Atomic Clock with Fluorescence Optical Pumping and Method using Same discloses conventional frequency control of an atomic clock system. The resonance cell is situated in a microwave cavity placed inside a solenoid that provides a static magnetic field which isolates the operative atomic resonance from other resonances that would increase the clock's sensitivity to extraneous magnetic fields. Various interactions of the atoms in the vapor cause a slight shift in the clock resonance frequency from what it would be if the atoms were isolated in free space. For example, the magnetic field influences the clock resonance frequency as the quadratic Zeeman shift. The energy of hyperfine energy states with non-zero Zeeman quantum number changes linearly with the static magnetic field strength. The energy of the hyperfine states with zero Zeeman quantum number changes quadratically with the static magnetic field strength. Additionally, the optical pumping light causes a change in the clock resonance frequency as a consequence of a phenomenon termed the AC Stark shift effect.
The clock resonance frequency perturbations are significant to the clock's operation, by altering the tick-rate slightly from what it would be in the absence of those perturbations. To a first approximation, though, the perturbations are not a problem for timekeeping, as the output frequency can be calibrated against a primary reference, such as a cesium atomic clock. Hence, even though the atomic tick-rate is not precise, its offset can be measured and accounted for. However, between periods of calibration, for example during satellite autonomy periods, any change in the perturbations would alter the atomic resonance frequency and would thereby degrade timekeeping.
Microwave power variation in combination with atomic vapor concentration variations can also affect the accuracy of the atomic clock. In the Rb atomic clock, the clock signal is derived from a vapor of atoms contained within a glass resonance cell. Not all regions of the vapor cell are equally illuminated by the microwave power source. In essence, there is a volumetric center region in the vapor gas cell which dominantly affects the clock signal, and which thereby dominantly affects the output frequency. In the gas cell atomic clock, changes in microwave power cause the center region to move. The microwave intensity and static magnetic field strength will be different for the atoms in the center region after it has moved, causing an apparent shift in the resonance frequency, and hence a change in the tick-rate. This particular dependence of the output frequency on microwave power is termed the position shift effect, and is more important to gas cell clock operation than other microwave power perturbations to the output frequency. Using standard methods of microwave power stabilization, there is no direct relationship between the microwave power exciting the atoms in the center region, and that measured by the microwave power detector.
It is desirable to stabilize the microwave power over long periods of time so that the atomic clock has improved accuracy. One straight forward technique, typically used in microwave electronics, is to convert a direct current (DC) microwave power measurement to a voltage, and then to stabilize this measured voltage against a reference voltage. In standard methods of microwave power stabilization, the microwave reference power level is derived from a stable voltage source. However, no reference voltage source presently available has the stability of an atomic clock's output frequency. The disadvantages to this approach are that the DC measurement is subject to low frequency noise and that the reference voltage may drift over time.
In the absence of the field all the atoms are in the ground state. However, as a consequence of interaction with the field some fraction of the atoms will be in the excited state. The degree of atomic excitation is conveniently described in terms of the relative atomic population imbalance Z. The imbalance extends from -1 when all the atoms are in the ground state to +1 when all the atoms are in the excited state, and between -1 and +1 when imbalanced due to excitations. Using a continuous wave field, the imbalance Z is a monotonically increasing function of intensity and asymptotes to a saturation value of zero at the saturation intensity. Moreover, the imbalance Z is a nonlinear function of field frequency.
Typically, when describing field-atom interactions, the strength of the interaction is parametrized by the Rabi frequency W. When an atom is initially in the ground state, and when a strong field is suddenly turned on, the atomic population will exhibit coherent oscillations between the ground and excited states so that the imbalance Z oscillates between +1 and -1. Eventually, the imbalance Z settles down to its equilibrium value of zero with a time constant determined by the two atomic states. This phenomenon is known as Transient Nutation. The oscillations are at the Rabi frequency W, which is proportional to the electromagnetic field-strength. When an atom or molecule is subjected to a frequency modulated resonant field, the resulting population variations show a resonant increase when the Rabi frequency of the excitation is approximately equal to the frequency modulation frequency Fm. Even though the Rabi resonance appears in a quantum system, it is not a typical resonance between atomic energy eigenstates. Rather, it is a dynamical resonance associated with a frequency match between the rate of a perturbation variation, that is the frequency modulation frequency Fm and an atomic internal rate of response to that perturbation at the Rabi frequency.
If the resonant field undergoes frequency modulation at a frequency modulation frequency Fm, the relative atomic population imbalance Z will again undergo an oscillation, this time, however, an undamped oscillation. Temporal variations of the imbalance Z occur at the fundamental modulation frequency and its harmonics because the imbalance Z is a nonlinear function of field frequency. Consequently, the response of the atomic system to the frequency modulated field of the microwave power source may be conveniently expressed in terms of a Fourier expansion. ##EQU1##
The amplitude of the second harmonic response (.nu..sub.2) will vary in response to varying intensity of the microwave power. The second harmonic has a high Q response to the Rabi frequency as shown in FIG. 2. The high Q second harmonic response of the atomic imbalance has a maximum when the Rabi frequency is twice the frequency modulated frequency Fm. Prior atomic systems have disadvantageously not stabilized the atomic frequency by not stabilizing the microwave power relying upon the second harmonic response of an atomic system when W=2 Fm. These and other disadvantages are solved or reduced using the invention.